What does the Pearson Chi-Square value mean?

I understand what d.f., alpha, and p-value all do but I don't understand what the Pearson Chi-Square (X^2) is showing.
Please explain?

Question

What does the Pearson Chi-Square value mean?

I understand what d.f., alpha, and p-value all do but I don't understand what the Pearson Chi-Square (X^2) is showing. 
Please explain?

anonymous · Answer

The Pearson $\chi^2$ is the test statistic used for categorical data. It's a value that represents your data in terms of the $\chi^2$ distribution, and it allows you to compare to the population (which is assumed to be $\chi^2$-distributed).

The value of $\alpha$, i.e. significance level of your test, tells you the critical values of $\chi^2$ (the cutoff points) for a $(1-\alpha)\times100\%$ confidence interval (assuming a two-tail hypothesis).

The test statistic will either fall inside or outside the confidence interval. In the former case, the null hypothesis is accepted, and in the latter, it is rejected.

Basically it comes down to a numerical portrayal of the frequencies of a given qualitative characteristic (like color).